They all moved towards the kitchen.

They moved towards the kitchen that they are attracted to. 'Graviate to or towards somebody or something' is a phrasal verb meaning 'move towards somebody or something that you are attracted to'.

I think you mean "gravitated." "The people gravitated with their drinks to the kichen" -> They all gradually moved towards the kitchen. Gravitate: 1. To move in response to the force of gravity. 2. To move downward. 3. To be attracted by or as if by an irresistible force: "My excuse must be that all Celts gravitate towards each other" (Oscar Wilde).

Gravity and gravitation - that which attracts things to other things. :) So the people had their drinks in hand, and all moved (gravitated) towards the kitchen. Just like how the Earth's gravity can pull in a wayward comet to destroy us all. Except these people probably enjoyed cake instead.